Question

Convert the pair of unlike fraction into its like fractions: $\frac{1}{18}$ and $\frac{3}{24}$

• A. $\frac{4}{72}$ and $\frac{9}{72}$
• B. $\frac{1}{18}$ and $\frac{9}{72}$
• C. $\frac{4}{72}$ and $\frac{3}{24}$
• D. $\frac{3}{54}$ and $\frac{12}{96}$

Answer 1

The correct option is A $\frac{4}{72}$ and $\frac{9}{72}$

To convert the unlike fractions into its like fractions, we need to find the LCM of denominators of the given fractions.

LCM of 18 and 24
18 can be written as $18=2\times 3\times 3$ and 24 can be written as $24=2\times 2\times 2\times 3$.

Taking the factors with highest powers common, we get
$3^2$ from 18 and $2^3$ from 24.

Multiplying them, we get $3^2\times 2^3=9\times 8=72$ as the required LCM.

Now, we multiply $\frac{1}{18}$ and $\frac{3}{24}$ with $4$ and $3$ respectively to make their denominators as $72.$

$\therefore \frac{1}{18}=\frac{1\times 4}{18\times 4}=\frac{4}{72}$

and $\frac{3}{24}=\frac{3\times 3}{24\times 3}=\frac{9}{72}$

$\therefore$ Option A is the correct answer